Does your ESP require a verified a sending domain/address?
Some ESPs (like SparkPost, Postmark, and SES) require a sender domain or sender address to be verified before emails can start going out. Double check that the From Address in your Delivery Settings matches your verified domain.
Are you using a test API key?
Some types of test API Keys don’t send emails, ensure you’re using the proper key. Learn more about API Keys here.
If you are using the proper key, check the logs to make sure your template doesn’t have any rendering errors.
Maybe the email was sent
Sometimes the email gets sent but ends up in your spam folder. If it’s not in spam, make sure you haven’t inadvertently unsubscribed yourself! Log into your ESP and make sure your email isn’t on the block list.